@parcel has it. The prohibited-transaction rules bar a sale or exchange of property between the plan and a disqualified person, full stop. Fair market value is not a defense, and an appraisal doesn't cure it. An entity you control is a disqualified person along with you, your spouse, and your lineal family, so the transaction you're describing is exactly the one the statute names.
The reason the rule is written that way is that self-dealing is hard to police case by case. Congress banned the category rather than asking whether each individual deal was fair. So the answer stays the same whether the price favors you, favors the IRA, or lands precisely on the appraisal.
What's at stake if it happens anyway: the IRA can be treated as fully distributed as of the first day of that tax year. On a six-figure account that's a tax bill measured in tens of thousands, plus early distribution consequences depending on your age, and it doesn't reverse.
The workable version is that the IRA buys from an unrelated third-party seller with IRA money, and you stay out of the chain entirely. People sometimes ask about selling the LLC property to a stranger and having the IRA buy a different property from a different stranger, which is fine, but back-to-back arrangements that end up putting your old asset in your IRA can be looked at as a step transaction. If you're anywhere near that line, have a tax attorney who works on prohibited transactions look at the actual facts before money moves.